Question 175 Problem Solving 2018 GMAT Official Guide

Question 175 Problem Solving 2018 GMAT Official Guide

Video explanation: If p is the product of the integers from 1 to 30, inclusive…

Comments

tarunsays

Hi , just a quick question
how did you get the total 14 and how did you derive those numbers like 1,1,2,1,1,2,1,1,3,1
and please give a proper explanation on how to solve a question if it says
1 to 100?

I am counting the number of 3s that are in the prime factorization of each of the multiples of 3 that are 30 or less. This because you are looking for the number of 3s in the prime factorization of $30!$. You can extend this to $100!$ as well. I go over the general concept in my lessons but I summarize the basic concept in the image attached below.

tarun says

Hi , just a quick question

how did you get the total 14 and how did you derive those numbers like 1,1,2,1,1,2,1,1,3,1

and please give a proper explanation on how to solve a question if it says

1 to 100?

GMAT Quantum says

I am counting the number of 3s that are in the prime factorization of each of the multiples of 3 that are 30 or less. This because you are looking for the number of 3s in the prime factorization of $30!$. You can extend this to $100!$ as well. I go over the general concept in my lessons but I summarize the basic concept in the image attached below.